Answer Key For The California Mathematics Standards
Grade 4
Introduction: Summary of Goals
GRADE FOUR
By the end of grade four, students understand large numbers and addition,
subtraction, multiplication, and division of whole numbers. They describe and
compare simple fractions and decimals. They understand the properties of, and
the relationships between, plane geometric figures. They collect, represent, and
analyze data to answer questions.
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
i.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.1: Students read and write whole numbers in the millions.
Write as numbers:
a. three million two hundred fifty-five thousand
3,255,000
b. seventy million
70,000,000
c. eight million two hundred thousand
8,200,000
d. four million eight hundred sixty-two thousand three hundred ten
4,862,310
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.2: Students order and compare whole numbers and decimals to two decimal places.
Write the letter that corresponds to each number that represents
the quantity on the number line:
B
A
0
C
D
1
2
3
1.
A
1.04
4.
B
0.40
2.
C
3.05
5.
E
3.50
3.
G
4.0
6.
D
1.4
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
E
G
4
1.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.3: Students round whole numbers through the millions to the nearest ten,
hundred, thousand, ten thousand, or hundred thousand.
a. Round off 5,185,924 to the nearest hundred:
5,185,900
b. Round off 5,185,924 to the nearest hundred
thousand:
c. Round off 5,185,924 to the nearest thousand:
5,200,000
5,186,000
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.4: Students decide when a rounded solution is called for and explain why such a
solution may be appropriate.
Buses need to be rented for 27 children going on a field trip. Each bus
can take 12 children in addition to the driver. How many buses must be
rented?
3 buses: Two buses will take only 24 children. One more bus must be
rented to take the 3 remaining children.
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
2.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.5: Students explain different interpretations of fractions: for example, parts
of a whole, parts of a set, and division of whole numbers by whole numbers; explain
equivalents of fractions (see Standard 4.0).
a.
Circle the picture below that shows 3 shaded
4
b. Circle the picture below in which 2/3 of the dots are small.
A. •
•
o
o
• • •
• • •
o o o
o o o
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
B • • • •
• • • •
o o o o
C. • • •
• • •
3.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.5: Students explain different interpretations of fractions: for example, parts
of a whole, parts of a set, and division of whole numbers by whole numbers; explain
equivalents of fractions (see Standard 4.0).
[CONTINUED]
c. Circle True or False
1 > 2.5
1. —
3
True
False
1
3
< 2.5
5 < 2.7
2. —
2
True
False
2.5
< 2.7
8 =—
2
3. —
12 3
True
False
2 x 4 = 8
12
4
3
3 < 10
4. —
—
7 21
True
False
3 x 3 = 9 < 10
7
3 21 21
1
<
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
4.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.6: Students write tenths and hundredths in decimal and fraction notations and
1
know the fraction and decimal equivalents for halves and fourths (e.g., 2 = 0.5 or .50;
7
3
4 = 1 4 = 1.75).
Write each fraction or mixed number as a decimal.
1
1
a. — =
.5
d. — =
4
2
3
25
b. — =
.3
e. 1
=
10
100
2
c. 11
=
11.02
100
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
.25
1.25
5.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.7: Students write the fraction represented by a drawing of parts of a figure;
represent a given fraction by using drawings; and relate a fraction to a simple decimal
on a number line.
a. Represent the fraction 3/5 using the figure below.
This is one way of showing 3/5
b. Write the letter that shows where each number goes on the number line:
A
C
0
1
1
3
10
0.3
B D
2
A
C
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
3
3.0
2
3 10
4
B
D
6.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.8: Students use concepts of negative numbers (e.g., on a number line, in
counting, in temperature, in “owing”).
Draw a number line and show -2 on it.
-4
-3 -2
-1
0
1
2
3
4
Number Sense 1.0
1.0: Students understand the place of whole numbers and decimals to two decimal places and
how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
NS 1.9: Students identify on a number line the relative position of positive
fractions, positive mixed numbers, and positive decimals to two decimal places.
Write the letter that represents where each number would go on the
number line:
a. 1 1
4
E
0
b. 2.50
1
2
A B C D E F G H I J
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
c. 3
4
J
C
3
K
7.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 2.0
2.0: Students extend their use and understanding of whole numbers to the addition and
subtraction of simple decimals.
NS 2.1: Students estimate and compute the sum or difference of whole numbers and
positive decimals to two places.
a. 14 - 3.21 = 10.79
b. 7..4 + 0..34 + 51 = 58.74
Number Sense 2.0
2.0: Students extend their use and understanding of whole numbers to the addition and
subtraction of simple decimals.
NS 2.2: Students round two-place decimals to one decimal or the nearest whole
number and judge the reasonableness of the rounded answer.
a. Round 3..19 to the nearest tenth.
3.2
b. Round 3..19 to the nearest whole number.
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
3
8.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 3.0: Students solve problems involving addition, subtraction, multiplication, and division of
whole numbers and understand the relationships among the operations.
NS 3.1: Students demonstrate an understanding of, and the ability to use, standard
algorithms for the addition and subtraction of multidigit numbers.
a. 60,000 - 241 = 59,759
b.
4,863 - 376 = 4,487
Number Sense 3.0: Students solve problems involving addition, subtraction, multiplication, and division of
whole numbers and understand the relationships among the operations.
NS 3.2: Students demonstrate an understanding of, and the ability to use, standard
algorithms for multiplying a multidigit number by a two-digit number and for dividing a
multidigit number by a one-digit number; use relationships between them to simplify
computations and to check results.
a. 37 x 302 = 11,174
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
b. 4
2,416 = 604
9.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 3.0: Students solve problems involving addition, subtraction, multiplication, and division of
whole numbers and understand the relationships among the operations.
NS 3.3: Students solve problems involving multiplication of multidigit numbers by
two-digit numbers.
There are bags of sand on a truck. Each bag of sand weighs 124
pounds. How many pounds do 38 bags weigh? 4,712 pounds.
Multiply the weight of 1 bag times the number of bags.
124 x 38 = 4,712 pounds
Number Sense 3.0: Students solve problems involving addition, subtraction, multiplication, and division of
whole numbers and understand the relationships among the operations.
NS 3.4: Students solve problems involving division of multidigit numbers by onedigit numbers.
There are 5,064 marbles that need to be packed in boxes. There are
6 boxes. We want to put the same number of marbles in each box.
How many marbles will fit into each box?
844
Divide the number of marbles by the number of boxes.
5,064 ÷ 6 = 844
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
10.
Answer Key For The California Mathematics Standards
Grade 4
Number Sense 4.0: Students know how to factor small whole numbers.
NS 4.1: Students understand that many whole numbers break down in different ways
(e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3).
You know that 1 x 30 = 30. List three other ways that you can write
30 as the product of two or more numbers:
5 x 6 = 30
3 x 10 = 30
2 x 15 = 30
Number Sense 4.0: Students know how to factor small whole numbers.
NS 4.2: Students know that numbers such as 2, 3, 5, 7 and 11 do not have any
factors except 1 and themselves and that such numbers are called prime numbers.
List all the prime numbers between 2 and 14:
3, 5, 7, 11, 13
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
11.
Answer Key For The California Mathematics Standards
Grade 4
Algebra and Functions 1.0: Students use and interpret variables, mathematical symbols, and properties
to write and simplify expressions and sentences.
AF 1.1: Students use letters, boxes or other symbols to stand for any number in simple
expressions or equations (e.g., demonstrate an understanding and the use of the concept
of a variable).
Tanya has read the first 78 pages of a 130 page book. Write an
expression to show the number of pages Tanya must read in order to
finish the book. Use a variable in your expression.
Let p be the number of pages left to read.
Then 78 + p = 130
Algebra and Functions 1.0: Students use and interpret variables, mathematical symbols, and properties
to write and simplify expressions and sentences.
AF 1.2: Students interpret and evaluate mathematical expressions that now use
parentheses.
If x = (a – b) - c and a is 10, b is 3 and C is 4, what is the value of x?
x=3
x = (10 - 3) - 4
x=7-4
x=3
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
12.
Answer Key For The California Mathematics Standards
Grade 4
Algebra and Functions 1.0: Students use and interpret variables, mathematical symbols, and properties
to write and simplify expressions and sentences.
AF 1.3: Students use parentheses to indicate which operation to perform first when
writing expressions containing more than two terms and different operations.
28 x (10 - 8) = 56
28 x 2 = 56
Algebra and Functions 1.0: Students use and interpret variables, mathematical symbols, and properties
to write and simplify expressions and sentences.
AF 1.4: Students use and interpret formulas (e.g., area = length xc width or A = lw)
to answer questions about quantities and their relationships.
Area = length x width.
a.
The length of a rectangle is 10 meters. The width is 4 meters.
What is the area? 40 square meters
Area = (10 x 4) m2
= 40m2
b.
The area of a rectangle is 200 square meters. The width is 10
meters. What is the length? 20 meters
A=LxW
200 = L x 10
L = (200 ÷ 10) meters
L = 20 meters
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
13.
Answer Key For The California Mathematics Standards
Grade 4
Algebra and Functions 1.0: Students use and interpret variables, mathematical symbols, and properties
to write and simplify expressions and sentences.
AF 1.5: Students understand that an equation such as y = 3x + 5 is a prescription
for determining a second number when a first is given.
Find y if y = 3 x + 5 and x = 4.
y = 17
y = 3x + 5
.
=3 4+5
= 12 + 5
= 17
“3x” means 3 times x.
Write the operation symbol
when the variable is
replaced by a number. The
order of operations states
that multiplication is done
before addition.
Algebra and Functions 2.0: Students know how to manipulate equations.
AF 2.1: Students know and understand that equals added to equals are equal.
Circle the statement that is true:
A 5 + 4 = 5 + (7 - 6)
4
5 + 1 = 5 + (1)
6 = 6
B. 5 + 5 = 5 + (5 - 4)
4
C. 5 + 4 = 5 + (4 + 4)
4
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
14.
Answer Key For The California Mathematics Standards
Grade 4
Algebra and Functions
Algebra and Functions 2.0: Students know how to manipulate equations.
AF 2.2: Students know and understand that equals multiplied by equals are equal.
Circle the statement that is true:
A. 5 (3 - 1) = 5 x 3 - 1
B. 5 (3 - 1) = 5 (1 + 1)
5(2) = 5(2)
10 = 10
C. 5 (3 - 1) = 5 + 3 + 1
Measurement and Geometry 1.0: Students understand perimeter and area.
MG 1.1: Students measure the area of rectangular shapes by using appropriate units,
such as square centimeter (cm2), square meter (m2), square kilometer (km2), square
inch (in2), square yard (yd2), or square mile (mi2).
Find the area of a rectangle that is 45 cm wide and 55 cm long:
Area
2,475cm2
A=LxW
A = 45cm x 55cm
= 2,475cm2
45cm
55cm
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
15.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 1.0: Students understand perimeter and area.
MG 1.2: Students recognize that rectangles that have the same area can have
different perimeters.
Do two rectangles with the same area necessarily have the same
perimeter? Give an example to support your answer.
No. Here are two examples. There are many others.
Both rectangles have equal areas
Area of A = 1 x 12
Area of B = 3 x 4
= 12 sq. units
= 12 sq. units
A
12
1
B
3
4
P = 2(L + W)
Perimeter of A = 2(12 + 1)
= 2(13)
= 26
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
Perimeter of B = 2(4 + 3)
= 2(7)
= 14
16.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 1.0: Students understand perimeter and area.
MG 1.3: Students understand that rectangles that have the same perimeter can have
different areas.
No. Here are two examples. There are many others.
A
5
B
10
12
P = 2(5 + 10)
= 2(15)
= 30
P = 2(3 + 12)
= 2(15)
= 30
3
Both rectangles have equal perimeters.
Area of A = L x W
= 10 x 5
= 50 sq. units
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
Area of B = L x W
= 12 x 3
= 36 sq. units
17.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 1.0: Students understand perimeter and area.
MG 1.4: Students understand and use formulas to solve problems involving
perimeters and areas of rectangles and squares; use those formulas to find the
areas of more complex figures by dividing the figures into basic shapes.
a. Use a formula to find the area
of this rectangle.
h = 7mm
Area = 91 sq. mm
b = 13 mm
A=hxb
= 7 x 13
= 91mm2
b. Find the area of the figure below. All angles are right angles.
Area = 14 sq. cm
2 cm
Square
One way is to divide the figure
into a square and a rectangle.
2 cm
3 cm
4 cm
Rectangle
2 cm
5 cm
Area of square = 2 x 2
= 4cm2
Area of rectangle = 5 x 2
= 10cm2
Total area = 4 + 10 = 14cm2
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
18.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 2.0: Students use two-dimensional coordinate grids to represent points and
graph lines and simple figures.
MG 2.1: Students draw the points corresponding to linear relationships on graph paper
(e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a
straight line).
On the graph, draw the first three points for the equation y = 3x
using 2, 3 and 4 as the values of x. Connect the points using a
straight line.
Organize the
information in a table.
x
2
3
4
3x
3.2
3.3
3.4
y
6
9
12
Then graph the points
(2,6), (3,9) and (4,12).
Connect with a straight
line.
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
y
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6
x
19.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 2.0: Students use two-dimensional coordinate grids to represent points and
graph lines and simple figures.
MG 2.2: Students understand that the length of a horizontal line segment equals the
difference of the x-coordinates.
What is the length of the line segment joining the points
Since the y-coordinates are equal,
(6, -4) and (21, -4)?
15
the length will be the difference in
the x-coordinates.
21 - 6 = 15
Measurement and Geometry 2.0: Students use two-dimensional coordinate grids to represent points and
graph lines and simple figures.
MG 2.3: Students understand that the length of a vertical line segment equals the
difference of the y-coordinates.
What is the length of the line segment joining the points
(121, 3) to (121, 17)?
14
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
Since the x-coordinates
are equal, the length will
be the difference in the
y-coordinates.
17 - 3 = 14
20.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 3.0: Students demonstrate an understanding of plane and solid geometric
objects and use this knowledge to show relationships and solve problems.
MG 3.1: Students identify lines that are parallel and perpendicular.
Write the word parallel under the lines that are parallel.
Write the word perpendicular under the lines that are perpendicular.
parallel
perpendicular
Measurement and Geometry 3.0: Students demonstrate an understanding of plane and solid geometric
objects and use this knowledge to show relationships and solve problems.
MG 3.2: Students identify the radius and diameter of a circle.
a.
In the circle below, draw a radius:
Here is one
example.
b.
In the circle below, draw a diameter:
Here is one
example.
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
21.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 3.0: Students demonstrate an understanding of plane and solid geometric
objects and use this knowledge to show relationships and solve problems.
MG 3.3: Students identify congruent figures.
Write the letter of the figure that is congruent with this figure:
A.
B.
C.
D
Measurement and Geometry 3.0: Students demonstrate an understanding of plane and solid geometric
objects and use this knowledge to show relationships and solve problems.
MG 3.4: Students identify figures that have bilateral and rotational symmetry.
Draw two lines of symmetry
through the equilateral triangle.
There are three lines of symmetry. Here are the possible
combinations of two lines of symmetry:
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
22.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 3.0: Students demonstrate an understanding of plane and solid geometric
objects and use this knowledge to show relationships and solve problems.
MG 3.5: Students know the definitions of a right angle, an acute angle, and an obtuse
angle; understand that 90º, 180º, 270º and 360º are associated, respectively, with
1 1 3
/4 , /2 , /4 , and full turns.
a.
An angle of less than 90 degrees is:
___ a right angle.
X an acute angle.
___
___ an obtuse angle.
b.
An angle of 1/4 turn is:
X
___
90°
___ 180°
___ 270°
___ 360°
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
23.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 3.0: Students demonstrate an understanding of plane and solid geometric
objects and use this knowledge to show relationships and solve problems.
MG 3.6: Students visualize, describe, and make models of geometric solids (e.g., prisms,
pyramids) in terms of the number and shape of faces, edges, and vertices; interpret
two-dimensional representations of three-dimensional objects; and draw patterns (of
faces) for a solid that, when cut and folded, will make a model of the solid.
a.
1. How many edges does a rectangular prism have?
12
2. How many vertices does a rectangular prism have?
1.
8
10
6
5
9
2.
7
11
2
3
4
12
6
5
7
8
12345678901234567890123
12345678901234567890123
12345678901234567890123
12345678901234567890123
12345678901234567890123
12345678901234567890123
12345678901234567890123
12345678901234567890123
3
8
2
1
1
4
b.
When this flat figure is folded to make a three-dimensional figure, the
shape will be a:
X cube
___
___ pyramid
___ cylinder
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
24.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 3.0: Students demonstrate an understanding of plane and solid geometric
objects and use this knowledge to show relationships and solve problems.
MG 3.7: Students know the definitions of different triangles (e.g., equilateral, isosceles,
scalene) and identify their attributes.
A.
B.
C.
Match the name with the triangle
Scalene
C
Isoceles
B
Right
A
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
25.
Answer Key For The California Mathematics Standards
Grade 4
Measurement and Geometry 3.0: Students demonstrate an understanding of plane and solid geometric
objects and use this knowledge to show relationships and solve problems.
MG 3.8: Students know the definition of different quadrilaterals (e.g., rhombus,
square, rectangle, parallelogram, trapezoid.
Mark each statement as true or false. Explain your answer:
a.
All squares are rectangles:
_X T
___ F
A square is a rectangle with all sides congruent.
b.
All rectangles are squares:
___ T
X
F
X
F
Not all rectangles have all sides congruent.
c.
All parallelograms are rectangles:
___ T
A parallelogram does not have to have all angles congruent.
d.
Every rhombus is a parallelogram:
X
T
___ F
A rhombus is a parallelogram with all sides congruent.
e.
All parallelograms are squares:
___ T
X
F
Parallelograms do not have to have all sides congruent.
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
26.
Answer Key For The California Mathematics Standards
Grade 4
Statistics, Data Analysis, and Probability 1.0: Students organize, represent, and interpret numerical
and categorical data and clearly communicate their findings.
S 1.1: Students formulate survey questions; systematically collect and represent
data on a number line; and coordinate graphs, tables, and charts.
These are the number of hours students did homework over the
weekend. Draw a bar graph to summarize the information.
student AR JC MT FR
hours
4
5
4
5
GS TB LM SG RT AL JS DC GN
4
2
1
4
0
2
5 4
3
CL JN
2 1
6
5
No. of
Students
4
3
2
1
0
0-2
3-4
5-6
Hours
0-2
3-4
5-6
Tally the hours. Then
construct a bar graph.
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
27.
Answer Key For The California Mathematics Standards
Grade 4
Statistics, Data Analysis, and Probability 1.0: Students organize, represent, and interpret numerical
and categorical data and clearly communicate their findings.
S 1.2: Students identify the mode(s) for sets of categorical data and the mode(s),
median, and any apparent outliers for numerical data sets.
Here are Jason’s scores on tests this term:
82
78
77
82
81
a. What is the median score?
81
b. What is the mode score?
82
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
28.
Answer Key For The California Mathematics Standards
Grade 4
Statistics, Data Analysis, and Probability 1.0: Students organize, represent, and interpret numerical
and categorical data and clearly communicate their findings.
S 1.3: Students interpret one- and two-variable data graphs to answer questions
about a situation.
Bill's Work in
School and at Home
50
40
30
20
10
0
Jan
Feb
Mar
= hours of school work
= hours of housework
a. How many hours of school work did Bill do in February?
40
b. In which month did Bill do more school work than housework?
January
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
29.
Answer Key For The California Mathematics Standards
Grade 4
Statistics, Data Analysis, and Probability 2.0: Students make predictions for simple probability situations.
S 2.1: Students represent all possible outcomes for a simple probability situation in an organized
way (e.g., tables, grids, tree diagrams).
Bill flips a coin and tosses a die. List all the possible outcomes.
1
Make a chart or tree diagram
2
3
Coin Die
H
1
H
2
H
3
H
4
H
5
H
6
Coin Die
T
1
T
2
T
3
T
4
T
5
T
6
4
H
Die
5
OR
6
Coin
1
2
T
3
4
Die
5
6
Statistics, data analysis, and probability 2.0: Students make predictions for simple probability situations.
S 2.2: Students express outcomes of experimental probability situations verbally
and numerically (e.g., 3 out of 4; ).
Jason tossed a coin repeatedly. Heads resulted from 32 of the tosses.
Tails resulted from 37 of the tosses. Write a fraction for the ratio of
heads to coin tosses.
heads
all tosses
32
heads + tails
Los Angeles County Office of Education: Mathematics
National Center to Improve the Tools of Educators
32
32 + 37
32
69
30.